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System size and network effects in a probabilistic herding model 

Simone Alfarano ,  Mishael Milakovic 

Christian-Albrechts-Universität Kiel, Kiel 24098, Germany

Abstract

We consider a generic probabilistic herding model that has previously been shown to suffer from the problem of N-dependence. The term N-dependence refers to the phenomenon that the unconditional distribution of the herding model approaches a Gaussian distribution (with decreasing variance) under enlargement of system size.

Starting from microscopic foundations, we first derive the analytical form of the unconditional distribution under a mean-field approximation. Second, in order to investigate the impact of network structure on the herding model, we study the behavior of the system under an enlargement of system size for different prototypical network structures.

Lo and behold, small-world and scale-free networks are not capable of overcoming the problem of N-dependence in the probabilistic herding model. As far as N-dependence is concerned, the relative communication range of agents turns out to be the crucial parameter of the herding model. 

 

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Related papers

Presentation: Oral at International Conference on Economic Science with Heterogeneous Interacting Agents 2008, by Mishael Milakovic
See On-line Journal of International Conference on Economic Science with Heterogeneous Interacting Agents 2008

Submitted: 2008-03-15 15:16
Revised:   2009-06-07 00:48